Getting Started

1. Open the Simulation: Launch the PDA-CFG Equivalence demonstration in your web browser
2. Review the Interface: The simulation displays tabbed views for PDA and CFG modes, shared language information, and interactive step-by-step execution
3. Choose Your Language: Use "Change Language" to select different context-free languages for exploration

Understanding the Interface

Dual-Model Visualization

• PDA Tab: Shows pushdown automaton with state diagram, visual stack, and transition selection
• CFG Tab: Displays context-free grammar with production rules, derivation tree, and rule selection
• Shared Information: Language description, test string, and remaining input visible in both modes

Navigation Controls

• Change Language: Switch between different language examples (aⁿbⁿ, palindromes, etc.)
• Previous Step: Undo the last transition or production rule application
• Show Hint: Get guidance on the correct next step for the current situation
• Apply Correct: Automatically execute the correct transition or production
• Reset: Return to the initial configuration for both PDA and CFG

Other Elements

• Action Choices: Multiple-choice selection for PDA transitions or CFG productions
• Visual Feedback: Immediate confirmation or correction of your selections
• Step Tracking: Complete execution history for both computational models

Step-by-Step Procedure

Step 1: Select Language Example

1. Use Change Language to choose from available context-free languages:

   • L = {aⁿbⁿ | n ≥ 0}: Equal numbers of a's followed by b's
   • L = {wwᴿ | w ∈ {a,b}*}: Palindromes over alphabet {a,b}
   • Additional language patterns as available

2. Review Language Description: Understand the formal definition and test string

3. Observe Initial Setup: Note the starting configurations for both PDA and CFG

Step 2: PDA Mode Execution

1. Switch to PDA Tab: Click the "Pushdown Automaton (PDA)" tab

2. Examine PDA Structure:

   • State Diagram: Visual representation of states and transitions
   • Visual Stack: Real-time display of stack contents
   • Current Status: Current state, remaining input, and stack configuration

3. Execute PDA Transitions:

   • Read Action Choices: Available transitions displayed as multiple-choice options
   • Select Transition: Choose the correct transition from 4 options
   • Observe Changes: Watch state changes, input consumption, and stack operations
   • Follow Progression: Continue until string is accepted or rejected

4. PDA Step Analysis:

   • Input Processing: See how each input symbol is consumed
   • Stack Operations: Observe push/pop operations maintaining computation history
   • State Transitions: Track movement through the automaton's state space

Step 3: CFG Mode Execution

1. Switch to CFG Tab: Click the "Context-Free Grammar (CFG)" tab

2. Examine CFG Structure:

   • Production Rules: Complete set of grammar productions
   • Derivation Tree: Visual tree showing string generation process
   • Current String: Current form in the derivation sequence

3. Execute CFG Derivations:

   • Select Productions: Choose appropriate production rules to apply
   • Apply Rules: Replace non-terminals according to selected productions
   • Build Derivation: Construct the complete derivation sequence
   • Reach Target: Continue until the target string is fully derived

4. CFG Step Analysis:

   • Rule Selection: Understand which production rules apply at each step
   • String Evolution: See how the string transforms through derivation
   • Tree Construction: Watch the parse tree grow with each application

Step 4: Equivalence Verification

1. Compare Execution Paths: Switch between PDA and CFG tabs to observe parallel recognition
2. Analyze Correspondence: Notice how PDA transitions correspond to CFG derivation steps
3. Verify Acceptance: Confirm both models accept/reject the same strings
4. Understand Mapping: See how stack operations relate to production rule applications